Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{t^2 - 2t - 8}{t^2 - 4t}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{t^2 - 2t - 8}{t^2 - 4t} = \dfrac{(t + 2)(t - 4)}{(t)(t - 4)} $ Notice that the term $(t - 4)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(t - 4)$ gives: $n = \dfrac{t + 2}{t}$ Since we divided by $(t - 4)$, $t \neq 4$. $n = \dfrac{t + 2}{t}; \space t \neq 4$